A sample of hydrogen exerts a pressure of 0.418 atm at 57.0° C. The gas is heated to 88.0° C at constant volume. What will its new pressure be?
Please show work
T1 = 273+ 57
T2 = 273 + 88
P1 = .418
V2 = V1
n and R constant so
n R/V = P/T = P1/T1 = P2/T2
P2 = .418 *(273+88)/(273+57)
(P1/T1) = (P2/T2)
You don't have the PVT formula memorized? You need to remember only 1.
Just remember P1V1/T1. Of course that's the same at new conditions of P2V2/T2. LOOK at P1V1/T1. If T is constant use your finger to cover up T and you're left with P1V1 = P2V2. If P is constant, use your finger to cover P and you're left with V1/T1 = V2/T2. If V is constant, cover the V and P1V1/T1 becomes P1/T1 = P2/T2. That makes it easy to remember.
so its 0.46
To determine the new pressure of the hydrogen gas, we can use the combined gas law equation:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
where:
P₁ = initial pressure of the gas
V₁ = constant volume
T₁ = initial temperature of the gas
P₂ = new pressure of the gas (what we want to find)
V₂ = constant volume
T₂ = new temperature of the gas (given)
Let's break down the equation using the given values:
P₁ = 0.418 atm
V₁ = constant volume (unknown)
T₁ = 57.0°C = 57.0 + 273.15 = 330.15 K
P₂ = new pressure of the gas (what we want to find)
V₂ = constant volume (unknown)
T₂ = 88.0°C = 88.0 + 273.15 = 361.15 K
Now, we'll rearrange the equation to solve for P₂:
P₂ = (P₁ * V₁ * T₂) / (V₂ * T₁)
Since the gas is heated at constant volume, V₁ = V₂. We can simplify the equation further:
P₂ = (P₁ * T₂) / T₁
Now, substitute the given values:
P₂ = (0.418 atm * 361.15 K) / 330.15 K
P₂ ≈ 0.4567 atm
Therefore, the new pressure of the hydrogen gas, when heated to 88.0°C at constant volume, will be approximately 0.4567 atm.